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We show that the spectral radius of nonnegative tensors can be approximatedwithin $\varepsilon$ error in polynomial time. This implies that the maximum ofa nonnegative homogeneous $d$-form in the unit ball with respect to$d$-H\"older norm can be approximated in polynomial time. These results arededuced by establishing bit-size estimates for the near-minimizers of functionsgiven by suprema of finitely many log-Laplace transforms of discretenonnegative measures on $\mathbb{R}^n$. Hence, some known upper bounds for theclique number of hypergraphs are polynomially computable.

Bit-complexity estimates in geometric programming, and application to the polynomial-time computation of the spectral radius of nonnegative tensors